Standard gear tooth form



Sept. 29, 1931. A. B. cox

STANDARD GEAR TOOTH FORM Filed Aug. 19, 1927 2 Sheets-Sheet l Sept. 29, 1931'. B CQX 1,825,621

' STANDARD GEAR TOOTH FORM Filed 7 2 Sheets-Sheet 2 INVENTOR if W v Patented Sept. 29, 1931 UNI-TED STATES ANTHONY BRUCE. COX, OIE WILKINSB'URG, PENNSYLVANIA STANDARD GEAR TOOTH FORM Application filed August 19, 1927. serial No. 214,039.

This standard of tooth would be about This invention relates to tooth-gearing, more particularly to a. method'of determininga' suitable standard. of tooth proportions for gear wheelshaving a constant total length {If of'load' carryin-gteeth in any given pair of wheels.

In Patent No. 1,525,642, granted to me February 10, 1925, I have described several v methods of designing gear wheel mechanism, in wherein an integral number of pairs of teeth are constantly in contact.

The present invention is directed to a method of determining the most suitable standard of tooth proportions for gear wheel mechanisms disclosed in the above mentioned patent which permits of standardizationpf the gear cutting or generating tools. for which they are made.

In the accompanying drawings constituting a part hereof and in which like'reference characters designate like parts, Fig. 1 is a diagrammatic view of a pair of gear wheels embodying the principles of this invention, and Figs; 2, 3 and 4 are similar views illustrating modifications of the form shown in Fig; 1 in accordance with variations intooth ratios and pressure angles.

In Fig. 1, I have illustrated a pan of gear wheels of241- teeth 1 to 1 ratio and pressure angle of 14 41 having a constant total length of load carrying teeth.

The most suitable standard of tooth proportions for a pair of wheels of this character may, in accordance with the present invention, be determined by the following formula Where Q is the form factor, n the number of teeth in the smaller of two meshing gear wheels, b the pressure angle, and M is the total number of pairs of teeth in contact in the pair of meshing gear wheels being con sidered. g, the form factor,-is the ratio of addendum length to circular pitch, or in symbols;

. g=a/P 18% longer than the standard Brown & Sharpe full depth tooth.

To choose the most suitable standard of tooth proportions I devise a table based upon a seriesof pressure angles, which angles are calculated by the following formula: cotangent n n cot (15 m- ;=0.l59154943a for which the corresponding values of g (form factor) are derived by means of the formula above. Using these formulas we may calculate the following table in which (X=percentage ratio of length of tooth to 1e th f standard Brown '& Sharpe gear tooth). n 0

Any one of these sets of values or still other sets calculated in the same way, may be selected as standard.

Referring to the table, the values of q and X% for 24 teeth and 1 1 41 standard pressure angle, are 0.3552 form factor and 113% for X these being the values of the set of gear wheels illustrated in Fig. 1. The values X are based on 100% for the standard Brown & Sharpe gear tooth so that 113 represents a tooth that is 18% longer than the Brown & Sharpe standard.

Two such gears meshing together would have exactly two pairs of teeth in contact (M =2), the length of the line of action along which tooth contact takes place (effective length) extending from the interference point a, Fig. 1, to the outside diameter of either gear, depending upon the direction of rotation of the gear wheels. Given the direction of rotation shown by the arrow in Fig. 1, this point is at b; a second contact is at 0. To secure llL=2 for any other speed ratio, such as 2 to 1 gear ratio, all that 1s necessary is to mesh the same 24 tooth pinion with a 48 tooth gear as illustrated in Vhen the pinion is cut, the hob or other ear generating tool automatically corrects for interference by cutting away the flank of the teeth up to the interference point, the cut away portion being all that part of the tooth that would otherwise be contacting along the line a-al. Therefore, the effective length of the line of action for a 2 to 1 gear ratio will be the same as in the 1 to 1 ratio illustrated in Fig. 1, namely, from the interference point d of the pinion to the point 5 on the outside diameter of the pinion.

From this it is obvious that the number of teeth in contact in any pair of meshing gear wheels in which the 24 tooth pinion is used is independent of the gear ratio, and is always two pairs of teeth (M 2). If in any case the integral number of pairs of teeth is not desired, any number of teeth other than 24, such as 15 or 32, can be cut in the pinion, the same as with present standard gearing. In such cases, where the expense is warranted, the special methods disclosed in the patent above referred to can be employed to obtain an integral number of pairs of teeth in contact, and 24 teeth in the pinion need not be used. Because of bearing wear, etc., which allows the gear bearing to separate, it would probably be best to choose a slightly larger pressure angle (say 15 in the 24 tooth standard) or whatever convenient fraction of an angle best judgment might indicate.

It will be noted in the foregoing table that the lowest value given for a is 17 teeth and a toot-h standard based on a pinion of less than 17 teeth is impractical without the use of long and short addendum because the teeth become so long as to be sharply pointed. For this reason and to avoid excessive undercutting it will be necessary to choose a stub tooth standard in case the pinion wheel has less than 17 teeth. Such a standard may be chosen by calculating a. table similar to the one above, except that it should be calculated for the value M =1 (on account of bearing wear use 1.01 or longer and the angle corresponding). The table is as follows If 12 teeth were chosen as standard, the pressure angle would be the same as for the 24 tooth standard but the teeth would be just one-half the length and therefore much stronger than if cut with the 24 tooth standard hob. However, the S tooth standard more nearly approximates present stub tooth standards and such a pair of gear wheels is illustrated in Fig. 3 of the drawings. As with the 24; tooth standard, any number of teeth may be out, say 12 or 20, but it is only when the 8 tooth pinion is used in any desired gear ratio that the integral number of pairs of teeth will be secured.

The M =1 standard teeth can be cut any desired depth if proper precautions are observed, for example, the 12 tooth standard shown in Fig. 4 can be cut the same depth as the 24 tooth standard, as is shown in dotted lines, except that the flanks of the teeth would be undercut excessively. To avoid the undercutting and to strengthen the root of the teeth the ordinary method of tip relief can be applied as indicated in the lower left of Fig. 4:. This relief would start at the point 0 of the gear teeth and should be sufficient in amount to prevent contact of this portion of the tooth curve with the flank portion of the teeth of the meshing gear under ordinary operating conditions. The tooth flanks can then be correspondingly strengthened, so long as contact is avoided.

The method of determining standard tooth forms as herein described, is applicable to spur gearing as has been demonstrated herein and also to helical, bevel, internal, long and short addendum gears, and other special cases of gearing.

It will be evident from the foregoing description of this invention that the method herein disclosed may be utilized in determining the most suitable standard of tooth proportions for gear wheel mechanisms having a constant total length of load carrying teeth in any given pair of meshing wheels.

I claim:

1. A toothed gearing comprising teeth having a form factor which is determined by the formula where g is the form factor which is the ratio of addendum length to circular pitch, or in symbols, g=a/P n the number of teeth in the smaller of two meshing gears, the pressure angle or cot =fb/'n'M and M, the total number of pairs of teeth in contact in a given pair of meshing wheels.

2. A toothed gearing as set forth in the next preceding claim, wherein a predetermined number of pairs of teeth are constantly in mesh.

3. A toothed gearing as set forth in claim its 1, wherein a constant total length of tooth is carrying the load at all times.

4:. A toothed gearing as set forth in claim 1, wherein a constant integral number of pairs 5 of teeth are in contact at all times.

In testimony whereof, I have hereunto set my hand.

ANTHONY BRUCE COX. 

